The present invention relates to a bandpass filter which uses active elements, that is, to an active bandpass filter, and more particularly to an active bandpass filter with improved degree of freedom in setting quality factor Q and peak gain.
FIG. 1 is a schematic circuit diagram an example of the configuration of a conventional bandpass filter. In this drawing, an input terminal 31 which accepts an input signal v.sub.i is connected to one end of a capacitor 32, which has a capacitance value of C.sub.31. The other end of the capacitor 32 is connected to one end of a resistor 33 which has a resistance value of R.sub.31, and also to one end of a resistor 34 which has a resistance value of R.sub.32. The other end of the resistor 33 is grounded. The other end of the resistor 34 is grounded through a capacitor 35 which has a capacitance value of C.sub.32, and is also connected to an output terminal 36 used to output an output signal v.sub.o.
In a filter circuit such as described above, the transfer function G(b/a) is given by equation (1). ##EQU1##
The cutoff frequency .omega..sub.0 is expressed by equation (2). ##EQU2##
The quality factor Q and the peak gain H are expressed by equation (3) and equation (4), respectively. ##EQU3##
However, in a conventional bandpass filter, such as shown in FIG. 1, there is a shortcoming in that the quality factor Q cannot be set to a value of 0.5 or higher. Another shortcoming is that it is not possible to have a peak gain H of 1 or higher.
If the substitutions C.sub.31 nC.sub.32 and R.sub.31 =mR.sub.32 (n, m&gt;0) are made in equation (2), the cutoff frequency .omega..sub.0 is expressed as in equation (5), so that the quality factor Q is expressed as in equation (6) . ##EQU4##
If we hold n constant and consider the maximum value of Q, it is seen by equation (7) that the value of Q is maximum when m=1/(n+1) . ##EQU5##
If we let Q.sub.max be this maximum value of Q, this value is expressed as follows. ##EQU6##
Therefore, the value of Q cannot be 0.5 or higher.
Equation (4) can be rewritten in the form of equation (9). Since C.sub.31, C.sub.32, R.sub.31, and R.sub.32 are all larger than zero, it is impossible for the peak gain H to be 1 or higher. ##EQU7##
To achieve superior filter characteristics, it is desirable to have a waveform as the output signal v.sub.o that changes sharply with respect to frequency, that is, it is desirable that the value of Q be made large. Enabling the setting of the peak gain H to a value of 1 or higher is also advantageous from the standpoint of circuit design.
Japanese laid-open patent No. 1989-067015 discloses a filter in that the values of quality factor Q and peak gain can be made larger than those of the conventional filter described above. This filter, however, includes complicated transformer-conductance amplifiers (variable voltage-current converters). Further, Japanese laid-open patent No. 1994-283965 discloses an active filter without variable voltage-current converters. This filter, however, is not an active bandpass filter but an active lowpass filter.